Prove that two triangles are congruent if two angles and the included

1.	Prove that two triangles are congruent if two angles and the included side of one triangle are equal to two angles and the included side of other trianglepls send the answer fast...........................I will mark it as brainliest
Answer» Given: Two triangles ABC and DEF such that B = E, C = F and BC = EF. To prove: ABC DEF Proof: Case I: If AB = DE then in ABC and DEF, AB = DE [by supposition] BC = EF [given] and B = E [given] Thus, ABC DEF [SAS criterion] Case II: If AB < DE TAKE a point G on ED such that EG = AB. Join GF. In ABC and GEF, we have AB = GE [by supposition] BC = EF [given] B = E [given] Thus, ABC GEF [SAS criterion] ACB = GFE [CORRESPONDING parts of congruent triangles are equal] But ACB = DFE [given] GFE =DFE, This is only POSSIBLE when FG coincides with FD or G coincides with D. AB must be equal to DE and hence, ABC DEF (by SAS) Case III: If AB > ED With a similar argument (as in case II), we may conclude that ABC DEF (by SAS) Thus, ABC DEF.

Prove that two triangles are congruent if two angles and the included side of one triangle are equal to two angles and the included side of other trianglepls send the answer fast...........................I will mark it as brainliest

Answer»

Given: Two triangles ABC and DEF such that B = E, C = F

and BC = EF. To prove: ABC DEF

Proof: Case I: If AB = DE then in

ABC and DEF, AB = DE [by supposition] BC = EF [given] and B = E [given]

Thus, ABC DEF [SAS criterion]

Case II: If AB < DE TAKE a point G on ED such that EG = AB.

Join GF. In ABC and GEF, we have AB = GE [by supposition] BC = EF [given] B = E [given] Thus, ABC GEF [SAS criterion]

ACB = GFE [CORRESPONDING parts of congruent triangles are equal]

But ACB = DFE [given] GFE =DFE,

This is only POSSIBLE when FG coincides with FD or G coincides with D.

AB must be equal to DE and hence, ABC DEF (by SAS) Case III: If AB > ED

With a similar argument (as in case II), we may conclude that ABC DEF (by SAS)

Thus, ABC DEF.